How many games does a NFL football team play at home in a season ?

8

Normally half games are home so 8

8

8 reg season games
2 preseason games

10 home games

8

It's always 8 every year unless they go to the playoffs.

Half of the schedule...which is 8...

It is 8 for every team this season except the Miami Dolphins. The Dolphins were considered the home team when they played the Giants at Wembly Stadium in London earlier this year. So they actually only play 7 games in their home stadium this year.

8 regular season plus up to 2 in the playoffs

8 regular season plus preseason plus playoffs minus overseas"home" games.
There is also the potential "disaster relocated" games that could be subtracted from the total.

8 during the regular season
10 if you include pre-season
12 if you include pre-season and playoffs

It's never the same for each team, but around 8 or 9 is normal.